Reordering of a Beamforming Matrix

ABSTRACT

Apparatuses, methods and systems for beamforming are disclosed. One embodiment of a method includes generating a beamforming matrix, including obtaining a channel matrix of a multiple-input, multiple-output (MIMO) between a multiple antenna transmitter and a receiver, determining an initial beamforming matrix based on a singular value decomposition of the channel matrix, generating a final beamforming matrix comprising re-ordering columns of the initial beamforming matrix for at least one sub-carrier of a multi-carrier signal based on a signal characteristic, processing a plurality of multi-carrier signals using the final beamforming matrix, and transmitting the processed plurality of multi-carrier signals through a plurality of transmit chains.

RELATED APPLICATIONS

This patent application claims the benefit of U.S. Provisional PatentApplication Ser. No. 61/976,070 filed Apr. 7, 2014, which is hereinincorporated by reference.

FIELD OF THE DESCRIBED EMBODIMENTS

The described embodiments relate generally to wireless communications.More particularly, the described embodiments relate to systems, methodsand apparatuses for reordering a beamforming matrix.

BACKGROUND

Transmit beamforming techniques have been used in many variations inmultiple-input, multiple-output (MIMO) systems. Typically, thesetechniques include the computation of a beamforming matrix at a receiverbased on a measurement of the transmission (MIMO) channel. When thematrix is communicated to the transmitter and applied by the transmitteron subsequent traffic, the effective received signal-to-noise ratio(SNR) for each stream in the MIMO system is improved resulting inimproved overall performance. While these solutions offer performanceimprovement by improving the effective SNR at the receiver, theinteraction between the distributions of SNRs across multiple antennachains and subcarriers, for different decoding and de-interleavingprocesses, and for data stream parsing and de-parsing are notconsidered. These interactions can lead to substantially degradedperformance compared to theoretically expected results.

It is desirable to have methods apparatuses, and systems for generatingbeamformed signals that account for the interactions between thedistributions of SNRs across multiple antenna chains and subcarriers,for different decoding and de-interleaving processes, and for datastream parsing and de-parsing.

SUMMARY

An embodiment includes a method of beamforming. The method includesgenerating a beamforming matrix, including obtaining a channel matrix ofa multiple-input, multiple-output (MIMO) between a multiple antennatransmitter and a receiver, determining an initial beamforming matrixbased on a singular value decomposition of the channel matrix, andgenerating a final beamforming matrix, wherein generating the finalbeamforming matrix includes re-ordering columns of the initialbeamforming matrix for at least one sub-carrier of a multi-carriersignal based on a signal characteristic.

At least some embodiments further include processing a plurality ofmulti-carrier signals using the final beamforming matrix, andtransmitting the processed plurality of multi-carrier signals through aplurality of transmitter chains.

Another embodiment includes an apparatus. The apparatus includes aplurality of receive chains, and a processor. The processor is operativeto obtain a channel matrix of a multiple-input, multiple-output (MIMO)channel between a multiple antenna transmitter and the plurality ofreceive chains, determine an initial beamforming matrix based on asingular value decomposition of the channel matrix, and generate a finalbeamforming matrix, wherein generating the final beamforming matrixincludes re-ordering columns of the initial beamforming matrix for aselected beamforming technique for at least one sub-carrier of amulti-carrier signal based on a signal characteristic.

For at least some embodiments, the transceiver includes the multipleantenna transmitter, and the processor is further operative tofacilitate processing of a plurality of multi-carrier signals using thefinal beamforming matrix, and the transceiver is operative to transmitthe processed plurality of multi-carrier signals through a plurality oftransmit chains.

For at least some embodiments, the transceiver is further operative totransmit the final beamforming matrix through a transmit chain back to asecond transceiver that includes the multiple antenna transmitter.

Other aspects and advantages of the described embodiments will becomeapparent from the following detailed description, taken in conjunctionwith the accompanying drawings, illustrating by way of example theprinciples of the described embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a first transceiver, a second transceiver, and a MIMOtransmission channel between the transceivers, according to anembodiment.

FIG. 2 shows a transmitter of a transceiver that includes K spatialstreams, N transmit antennas, and beamforming processing, according toan embodiment.

FIG. 3 shows a receiver portion of a transceiver that includes Mreceiver antennas, and beamforming matrix processing, according to anembodiment.

FIG. 4 shows the performance of MCSO with different singular valuere-ordering schemes in CMD (channel model D provided by IEEE formodeling Wireless LAN propagation environment) channels, according to anembodiment.

FIG. 5 shows packet errors statistics of MCSO across 100 CMD channelswith different re-ordering schemes, according to an embodiment.

FIG. 6 shows a performance of MCS7 with different singular valuere-ordering schemes in CMD channels, according to an embodiment.

FIG. 7 shows packet errors statistics of MCS7 across 100 CMD channelswith different re-ordering schemes, according to an embodiment.

FIG. 8 shows electronic circuitry for generating LLRs (log-likelihoodratios), and graphs that depict the corresponding confidence levels withdifferent schemes of reordering a beamforming matrix, according to anembodiment.

FIG. 9 shows a plot of confidence levels of LLRs over time after beingde-interleaved and stream de-parsed with different reordering schemes,according to an embodiment.

FIG. 10 shows a zoomed (enlarged) version of FIG. 9, according to anembodiment.

FIG. 11 shows a run-length (contiguous sequence with confidence levelbelow a confidence threshold) distribution of consecutive confidencelevels of the LLRs below the confidence threshold for a firstre-ordering scheme A.

FIG. 12 shows a run-length (contiguous sequence with confidence levelbelow a confidence threshold) distribution of consecutive confidencelevels of the LLRs below the confidence threshold for a secondre-ordering scheme B.

FIG. 13 is a flow chart that includes steps of a method of beamforming,according to an embodiment.

DETAILED DESCRIPTION

The embodiments described include methods, apparatuses, and systems forreducing the implementation loss (that is, performance loss relative toa theoretical limit) of beamforming resulting from the interactionbetween the signal-to-noise-ratios (SNRs) across multiple antenna chainsand subcarriers, the decoding and de-interleaving, and/or stream parsingand de-parsing processes of multi-carrier, multiple-input,multiple-output (MIMO) communications. At least some embodiments includedynamically adjusting computation of a beamforming matrix based on thespecific interplay between a measured MIMO channel, the de-interleavingand decoding, stream parsing and/or de-parsing processes resulting inbetter performance (that is, lower Packet Error Rate) than traditionalMIMO beamforming techniques.

At least some embodiments include determining a final beamforming matrixby a processor of a transceiver re-ordering columns of an initialtransmit matrix. For one embodiment, the transceiver transmits the finalbeamforming matrix back to second transceiver that applies the finaltransmit matrix to multiple spatial transmit streams. For anotherembodiment, the transceiver applies the final transmit matrix tomultiple spatial transmit streams of the transceiver.

FIG. 1 shows a first transceiver 110, a second transceiver 120, and aMIMO transmission channel between the transceivers 110, 120, accordingto an embodiment. As shown, the first transceiver 110 includes Nantennas transmitting communication signals, and the second transceiver120 includes M antennas receiving communications signals. Accordingly,the transmission channel between the first transceiver 110 and thesecond transceiver 120 can be characterized by an M×N channel matrix H.

For an embodiment, the transmission signals between the firsttransceiver 110 and the second transceiver 120 include multi-carriermodulation signals. Multi-carrier modulation (MCM) is a method oftransmitting data by splitting it into several components, and sendingeach of these components over separate carrier signals. The individualcarriers have narrow bandwidth, but the composite signal can have broadbandwidth. The advantages of MCM include relative immunity to fadingcaused by transmission over more than one path at a time (multipathfading), less susceptibility than single-carrier systems to interferencecaused by impulse noise, and enhanced immunity to inter-symbolinterference.

An exemplary form of MCM includes orthogonal frequency-divisionmultiplexing (OFDM). OFDM is essentially identical to coded OFDM (COFDM)and discrete multi-tone modulation (DMT), and is a frequency-divisionmultiplexing (FDM) scheme used as a digital multi-carrier modulationmethod. The primary advantage of OFDM over single-carrier schemes is itsability to cope with severe channel conditions (for example, narrowbandinterference and frequency-selective fading due to multipath) withoutcomplex equalization filters. Channel equalization is simplified becauseOFDM may be viewed as using many slowly modulated narrowband signalsrather than one rapidly modulated wideband signal. The low symbol ratemakes the use of a guard interval between symbols affordable, making itpossible to eliminate intersymbol interference (ISI) and utilize echoesand time-spreading to achieve a diversity gain, that is, asignal-to-noise ratio improvement.

An embodiment includes obtaining a channel matrix H per sub-carrier of amulti-carrier signal. For an embodiment, the channel matrix isdetermined at the receiver, and communicated back to the transmitter.However, for another embodiment, the channel matrix is determined at thetransmitter. That is, by assuming reciprocity of the transmissionchannel, signals received by the transmitting transceiver from thereceiving transmitter can be used to determine the channel matrix H.

An embodiment includes performing a SVD (singular value decomposition)matrix decomposition H=USV^(H) for each subcarrier. That is, the SVDdecomposition is based on the previously described channel matrix H. Foran embodiment of the SVD matrix decomposition:

-   -   U is a left singular vector matrix;    -   S is a singular value matrix; and    -   V is a right singular vector matrix (for an embodiment, this is        the beamforming matrix applied at the transmitter).

It is to be noted, that for at least some of the described embodiments,S is diagonal matrix with each of the diagonal values corresponding to asingular value. Further, there are many possible methods to realize thedecomposition. Depending on the technique, different ordering ofsingular values (that is, the diagonal elements of the S matrix) canresult. For an embodiment, the diagonal elements increase in magnitudetraversing down the diagonal of the S matrix. For another embodiment,the diagonal elements decrease in magnitude traversing down the diagonalof the S matrix. Without loss of generality, at least some of thedescribed embodiments assume that the diagonal elements of S are indecreasing order traversing down the diagonal.

For at least some embodiments, the right singular vector matrix, V, isused as an initial beamforming matrix. If this matrix is applied at thetransmitter, then the effective channel seen at the receiver isH*V=USV^(H)V=US. The received signal at a particular subcarrier can bedenoted as Y=HVX+N, where VX is the beam-formed transmitted data and Nis the additive noise. Since U is orthonormal, after pre-multiplicationof Y by U^(H) at the receiver, the effective received vector can writtenas Y_(eff)=U^(H)Y=SX+U^(H)N. Thus, since S is diagonal, each of themultiple transmitted streams can be detected independently.Additionally, the signal quality or SNR on each stream is determined bythe corresponding singular value. For instance, if there are twotransmitted streams in a 2×2 system, a first transmitted stream's SNR isbased on the first singular value of S (that is, S(1,1)) and a secondtransmitted stream's SNR is based on the second singular value of S(that is, S(2,2)). If the streams are decoded completely independently,the link performance is dictated by the stream with the worse SNR. Sincethe channel can be different for each subcarrier in an OFDM system, ifthe higher of the two SNRs resulting from the singular values of the Smatrix for each subcarrier can be distributed between the streamsevenly, then the resulting discrepancy in average SNR across bothstreams could be reduced, thereby improving the error of the worststream and hence improving overall link performance.

Even for the case where the streams are jointly decoded, judiciouslydistributing the higher/highest SNRs among the streams across thesubcarriers can improve the overall link performance.

Reordering the columns of the initial beamforming matrix is one methodof generating a final beamforming matrix which can be used to multiplythe transmit data and thereby improve link performance compared to usingthe initial beamforming matrix to multiply the transmit data.

FIG. 2 shows a transmitter of a transceiver that includes K spatialstreams, N transmit antennas, and beamforming processing, according toan embodiment. As shown, a stream of data (source data) is received bythe transmitter portion, which is encoded by an encoder 210, parsed intomultiple (K) spatial data streams by a parser 215, and interleaved by aninter-leaver 220. The plurality of K spatial streams includes Nmodulators 230, 240. Multiplication of the K spatial streams by abeamforming matrix, 270, results in the data which is transmitted by Ntransmit chains 290 from the N multiple transmit antennas TX1, TX2 . . .TXN.

For an embodiment, the final beamforming matrix is determined elsewhere(for example, at a receiver of the K spatial streams) and thencommunicated to the transmitter. Based on the channel matrix H and thefinal beamforming matrix, a processor 280 of the transceiver 200 uploadsthe coefficients of the final beamforming matrix to a beamforming matrixmultiplier 270. For another embodiment, the final beamforming matrix isgenerated at the transmitter if the previously describe reciprocity ofthe transmission channel is assumed. It is to be understood that whilethe beamforming matrix multiplier is 270 depicted as a separatefunctional block, for at least some embodiments that processing providedby the beamforming matrix multiplier is 270 is incorporated into theprocessing of the processor 280. For at least some embodiments, theprocessor 280 facilitates the processing

For at least some embodiments, generating the final beamforming matrixincludes obtaining the channel matrix (H) of a multiple-input,multiple-output (MIMO) channel between a multiple antenna transmitterand a receiver, determining an initial beamforming matrix based on asingular value decomposition of the channel matrix. Finally, the finalbeamforming matrix is generated by re-ordering columns of the initialbeamforming matrix for at least one sub-carrier of a multi-carriersignal based on a signal characteristic.

Once the final beamforming matrix has been generated, a plurality ofmulti-carrier signals are processed using the final beamforming matrix(that is, for example, through the beamforming matrix multiplier 270),and the processed plurality of multi-carrier signals are transmittedthrough a plurality of transmit chains of the multiple antennatransmitter.

Re-Ordering of Columns of the Initial Beamforming Matrix

For an embodiment, one or more of various signal characteristics can beused for determining how to re-order columns of the initial beamformingmatrix. For an embodiment, the re-ordering of the columns is dependenton the modulation and coding schemes used for transmission. For at leastsome embodiments, the re-ordering of the columns is performed on asub-carrier basis of the multi-carrier transmission signal.

FIG. 3 shows a receiver portion of a transceiver 300 that includes Mreceive antennas, and beamforming matrix processing, according to anembodiment. For this embodiment, the receiver portion of a receivingtransceiver performs the processing and determination of the finalbeamforming matrix. As shown, the receiver includes M receive antennasthat receive the K spatial streams transmitted by the transmittingtransceiver.

A MIMO detector 310 processes the received signals, and generates areceived bit stream. A decoder 320 decodes the received bit stream,ideally yielding the K spatially separate streams of bits. Processingthe received signals, includes estimation of the channel and noise (330)which is subsequently used to equalize and decode the signal resultingin the decoded bit stream.

The channel and noise estimator 330 also performs a channel qualityestimation, which can be used to determine the modulation and codingschemes used for transmission. For an embodiment, a look up table (LUT)350 is accessed that provides a modulation and coding scheme for adetermined channel quality. For an embodiment, the channel and noiseestimator 330 generates the channel matrix H.

An SVD decomposition block 340 performs the previously described SVDdecomposition, yielding an initial beamforming matrix.

Once the modulation and coding schemes having been determined, anembodiment includes re-ordering the columns (360) of the initialbeamforming matrix based on the modulation and coding scheme.

As described, for embodiments, the initial Singular Value matrix S isre-ordered to S′ based on various metrics. For an embodiment, thisincludes computing a new beamforming matrix V′ based on S′. Note that V′is obtained by shuffling the columns of V. So, in practice, S′ does nothave to be computed/determined. If the desired reordering is known, V′can be obtained from V by shuffling the columns corresponding to thedesired reordering. Although the discussion regarding reordering belowis described in terms of reordering singular values of the S matrix, thediscussion equivalently applies to reordering columns of V as well. Oneadvantage of doing the permutation on V is that the transmitter (whichhas more direct knowledge of MCS, coding, etc.) can choose permutationbased on those parameters.

For an embodiment, the column re-ordering of the initial beamformingmatrix is based on the modulation and coding scheme being used on atransmission packet. If there is a set of known MCS a priori, a lookuptable (MCS LUT 350) can be used based on MCS for the current packet, todetermine the reordering scheme for the next packet, or a set of nextpackets.

The described embodiments include different possible reordering schemesfor multi-carrier modulation. For an embodiment, selecting a beamformingtechnique includes singular value decomposition (SVD), wherein aninitial beamforming matrix includes at least one of Ascending Value SVD(AVSVD) that includes diagonal singular values in an increasing order,or Descending Value SVD (DVSVD) that includes diagonal singular valuesin a decreasing order. Further, for an embodiment, if the initialbeamforming matrix includes AVSVD, then the final beamforming matrixincludes DVSVD, and if the initial beamforming matrix includes DVSVD,then the final beamforming matrix includes AVSVD. That is, for at leastsome embodiments, all of the sub-carriers of the multi-carrier signalsuse the conventional SVD (DVSVD) to determine the initial beamformingmatrix. That is, singular values in decreasing order.

At least some embodiments include identifying a number of possiblepermutations of the re-ordering of columns to be a number N, dividingthe total number of subcarriers into N sets, and re-ordering columns ofthe initial beamforming matrix according to a one of the N permutationsfor at least a subset of the N sets. There are several examples of howthis embodiment may be realized. For at least some embodiments,alternating sub-carriers use different reordering such that sub-carrierswith even indexing have singular values in decreasing order whilesub-carriers with odd indexing have singular values in increasing order.For at least some embodiments, a first half of the sub-carriers use theconventional SVD, that is, have singular values in decreasing orderwhile remaining half use modified SVD, that is, have singular values inincreasing order. For at least some embodiments, a first half of thesub-carriers use the modified SVD, that is, have singular values inincreasing order while remaining half use conventional SVD, that is,have singular values in decreasing order. Although above examplesdescribe reordering using N=2 permutations (increasing order, decreasingorder), possible reordering schemes can be extended to larger values ofN.

For at least some embodiments, the performance of different MCS(modulation and coding schemes) formats can be analyzed with differentre-ordering schemes, such that an optimal reordering scheme exists foreach MCS format. This analysis can be used to develop look up tables forfurther processing.

For example, in the 802.11n/ac system, for the 20 MHz bandwidth casewith 2 spatial streams where convolutional coding is used, MCS schemes0, 1, 2, 3, 4, 6 and 8 (per the IEEE 802.11ac standard) perform betterwhen simulated across a large set of dispersive channels when thesingular values are ordered in decreasing order, while in MCS schemes 5and 7, an improved performance is observed when the singular values areordered in increasing order. The table below summarizes the modulationand coding rate used for the aforementioned MCS schemes and thepreferred reordering scheme. The MCS and associated transmission signalcharacteristics are based on the IEEE 802.11ac standard, as depicted inthe following table.

Preferred singular MCS Modulation Coding Rate value ordering 0 BPSK ½Decreasing 1 QPSK ½ Decreasing 2 QPSK ¾ Decreasing 3 16-QAM ½ Decreasing4 16-QAM ¾ Decreasing 5 64-QAM ⅔ Increasing 6 64-QAM ¾ Decreasing 764-QAM ⅚ Increasing 8 256-QAM  ¾ Decreasing

Although each MCS is designated above using modulation and coding rate,there are other elements of the transmission signal such as theinterleaver, mapper, puncturer, parser which all play a role indetermining which reordering scheme will improve the performance. Theabove table chooses among a set of N=2 reordering schemes. However, theperformance comparison can be extended to a larger set of reorderingschemes.

FIG. 4 shows a performance of MCSO with different singular valuere-ordering schemes in CMD (channel model D provided by IEEE formodeling Wireless LAN propagation environment) channels. FIG. 5 showspacket errors statistics of MCSO across 100 CMD channel realizationswith different re-ordering schemes. FIG. 6 shows a performance of MCS7with different singular value re-ordering schemes in CMD channels. FIG.7 shows the packet errors statistics of MCS7 across 100 CMD channelswith different re-ordering schemes.

The reordering schemes described above involve partitioning thesubcarriers into sets and use a chosen reordering scheme for each set.Alternatively, the reordering scheme can be chosen more individually ona per subcarrier basis using additional criteria which examine theimpact of other elements of the transmitter used to construct the signalsuch as the interleaver and the parser. Due to the interplay of theseelements with the SNR of each subcarrier, certain susceptible portionsof the signal fed to the decoder are more likely to cause decodingerrors. Identifying such susceptible portions of the signal stream andthen adjusting reordering schemes on specific subcarriers which canreduce the likelihood of those susceptible portions, and applying thebeamforming matrix based on the adjusted reordering can lead to improvedreceiver performance.

An embodiment includes constructing de-interleaved and or streamde-parsed sequence of effective SNRs based on singular values (assumingthe default decreasing order of singular values) per subcarrier andstream. This embodiment further includes finding all sequences ofconsecutive SNRs below an SNR threshold. Further, this embodimentincludes rearranging singular value ordering on at least one of thesubcarriers corresponding to the locations in the aforementionedsequences such that the number of such sequences with SNRs below the SNRthreshold is reduced.

An embodiment includes cycling through a set of possible S′ permutationsacross adjacent subcarriers and repeat cycle to cover all subcarriers.Idea here is that by statistically evening out the distribution of highand low singular values across subcarriers, the de-interleaved signalwill have lower likelihood of long sequence of low LLRs.

An embodiment includes letting the number of possible permutations of Sbe some number N. Divide the total number of subcarriers into Ncontiguous sets. For each set use one permutation of S. Again, as notedabove, after de-interleaving, this approach may also result in a lowerlikelihood of long sequence of low LLRs. Note that low LLR is correlatedwith a low effective SNR. A simple 2×2 MIMO system can be used toillustrate. For an embodiment, the effective received vector on a chosensubcarrier is given by;

Y _(eff) =U ^(H) Y=SX+U ^(H) N

Since S is a diagonal matrix of singular values with positive and realvalues, s₁₁ and s₂₂ and U is a unitary matrix, the above decompositionprovides two parallel channels, that is;

y _(eff,stream1) =s ₁₁ x ₁ +n ₁

y _(eff,stream2) =s ₂₂ x ₂ +n ₂

where, x1 and x2 are the transmitted data on stream 1 and stream 2respectively, and n1 and n2 are the complex Gaussian noise terms eachwith variance σ².

Note that the effective SNRs on stream 1 and stream 2 are proportionalto |s₁₁|² and |s₂₂|² respectively.

To show the relation between SNR and LLRs, a simple modulation andcoding scheme can be considered, such as MCSO that uses BPSK modulation.The Log-likelihood ratio for a bit on stream 1 and stream 2 (for thecase where the noise is white and Complex Gaussian) can be shown to be;

$\begin{matrix} {{L\; L\; R_{{stream}\; 1}} = {{( {4\text{/}\sigma^{2}} ) \cdot {Re}}\{ {y_{{eff},{{stream}\; 1}}*s_{11}} )}} \} \\{= {( {4\text{/}\sigma^{2}} ) \cdot ( {{{{s_{11}}^{2} \cdot {Re}}\{ x_{1} \}} + {{s_{11} \cdot {Re}}\{ n_{1} \}}} )}} \\{{L\; L\; R_{{stream}\; 2}} = {{( {4\text{/}\sigma^{2}} ) \cdot {Re}}\{ {y_{{eff},{{stream}\; 2}}*s_{22}} \}}} \\{= {( {4\text{/}\sigma^{2}} ) \cdot ( {{{{s_{22}}^{2} \cdot {Re}}\{ x_{2} \}} + {{s_{22} \cdot {Re}}\{ n_{2} \}}} )}}\end{matrix}$

Hence, it can be observed from the above relations, that the LLRs areclosely related to the singular values s₁₁ and s₂₂ and hence the SNRs oneach stream. Specifically, the SNRs are proportional to the square ofthe singular values. Additionally, the higher the singular value, thehigher the confidence level or equivalently LLR since the transmittedsymbol is effectively multiplied by the square of the singular valuewhile the noise is only multiplied by the singular value. An embodimentincludes adjusting reordering across subcarriers such that the maximumnumber of subcarriers across any stream less than a threshold isminimized.

FIG. 8 shows electronic circuitry for generating LLRs, and graphs thatdepict the corresponding confidence levels before and after reordering abeamforming matrix, according to an embodiment. Confidence levels arecomputed based on knowledge of the SNR for a subcarrier along with themapper used to map the bits to a constellation point by the transmitter.As shown, an FFT 810 receives a stream of bits of a received signal. Theoutput of the FFT 810 is equalized by an equalizer 820. For the Kspatial streams, K FFTs and K equalizers generate K streams of LLRs. TheK streams of LLRs are then de-interleaved by K de-inter-leavers 830,832. The outputs of the de-inter-leavers 830, 832 are received andde-parsed by a de-parser 840, generating a stream of LLRs. That is, ade-parsed, de-interleaved sequence of confidence levels is constructedbased on singular values per subcarrier of the plurality spatial streamsof the MIMO channel. In this example, a single stream of LLRs is shownafter de-parsing since a single convolutional encoder is used. For thecase where multiple convolutional encoders are used, the resultingnumber of stream(s) of LLRs will be equivalent to the number ofconvolutional encoders. Additionally, when the number of spatial streamsis equal to the number of convolutional encoders and each encoder'soutput is mapped to a spatial stream (that is, 1 to 1 mapping between anencoder and a spatial stream), the parser essentially becomes apass-through or is non-existent. In this case, the de-parser is notrequired.

A first plot 850 depicts confidence levels of the stream of LLRs overtime after being de-interleaved. As shown, a portion of the plot fallsbelow a confidence threshold. The width W of this portion is dependenton how many consecutive confidence levels fall below the confidencethreshold. That is a contiguous sequence of confidence levels in thede-interleaved sequence are identified, wherein each of the confidencelevels in the contiguous sequence is below the confidence threshold andnumber of confidence levels in the contiguous sequence exceeds arun-length threshold, wherein the run-length threshold is chosen basedon properties of a convolutional code used by the transmitter. Furtherreordering of the columns of the initial beamforming matrix of at leastone of the subcarriers reduces a number of confidence levels incontiguous sequences of the de-interleaved sequence that are below theconfidence threshold to be below the run-length threshold as shown bythe second plot 860. That is, the W1 and W2 have run-lengths less thanthe run-length threshold due to the re-ordering of the columns of theinitial beamforming matrix.

FIG. 9 depicts a plot of confidence levels of LLRs over time after beingde-interleaved with different reordering schemes. FIG. 10 is a zoomedversion of FIG. 9 and it can be observed that in reordering scheme B,the result is a sequence with consecutive low confidence level. Such asequence of consecutive low confidence level could be detrimental in thedecoding process, thereby causing packet failure.

FIG. 11 and FIG. 12 depict the run-length (contiguous sequence withconfidence level below a confidence threshold) distribution ofconsecutive confidence levels of the LLRs below the confidence thresholdfor a first re-ordering scheme A and second re-ordering scheme B. Notethat in reordering scheme B, there are significant number ofsub-sequences that have consecutive confidence levels below a confidencethreshold. This can lead to higher packet error rates. For example, if acode can correct continuous burst of up to say, D=5 errors, thenreordering scheme B is worse compared to scheme A since there are manybursts in the confidence level sequence that have run-lengths greaterthan D. Hence using reordering scheme A is better justified whencompared to reordering scheme B.

FIG. 13 is a flow chart that includes steps of a method of beamforming,according to an embodiment. A first step 1310 includes obtaining achannel matrix of a multiple-input, multiple-output (MIMO) between amultiple antenna transmitter and a receiver. A second step 1320 includesdetermining an initial beamforming matrix based on a singular valuedecomposition of the channel matrix. A third step 1330 includesgenerating an final beamforming matrix comprising re-ordering columns ofthe initial beamforming matrix for a selected beamforming technique forat least one sub-carrier of a multi-carrier signal based on a signalcharacteristic.

A fourth step 1340 includes processing a plurality of multi-carriersignals using the final beamforming matrix. A fifth step 1350 includestransmitting the processed plurality of multi-carrier signals through aplurality of transmit chains. It is to be understood that for anembodiment, the steps 1310, 1320, 1330, 1340 and 1350 can all becompleted within a single transceiver. However, for other embodiments,the steps may be completed at multiple transceivers. For example, steps1310, 1320, 1330 can be completed at a receiving transceiver, and steps1340, 1350 can be completed at a transmitting transceiver.Alternatively, steps 1310, 1320 can be completed at a receivingtransceiver and steps 1330, 1340, 1350 can be completed at atransmitting transceiver.

As described, for an embodiment, the signal characteristic includes amodulation and coding schemes. For an embodiment, the re-ordering of thecolumns of the initial beamforming matrix is performed using a currentpacket of the multicarrier signals. For an embodiment, once themodulation and coding scheme is identified, a column re-ordering schemeis determined by accessing a look-up-table (LUT) based on the identifiedmodulation and coding scheme.

For an embodiment, the re-ordering of the columns of the initialbeamforming matrix is performed based on a current packet of themulticarrier signals. For at least some embodiments, the beamformingmatrix is computed based on the current packet. However, the beamformingmatrix cannot be applied until the next transmitted packet by thetransmitting transceiver.

For an embodiment, the columns of the initial beamforming matrix arere-ordered upon changes of the signal characteristic. For an embodiment,the signal characteristic includes a data rate.

An embodiment further includes constructing de-interleaved sequences ofconfidence levels for each spatial stream of a plurality of spatialstreams of the MIMO channel based on singular values per subcarrier ofeach spatial stream, wherein the confidence levels include functions ofSNRs (signal to noise ratios), constructing a de-parsed sequence ofconfidence levels from the de-interleaved sequences, and identifying acontiguous sequence of confidence levels in the de-parsed sequence,wherein each of the confidence levels in the contiguous sequence isbelow a confidence threshold and number of confidence levels in thecontiguous sequence exceeds a run-length threshold. The reordering ofthe columns of the initial beamforming matrix of at least one of thesubcarriers reduces a number of confidence levels in contiguoussequences of the de-parsed sequence that are below the confidencethreshold to be below the run-length threshold. For an embodiment, therun-length threshold is based on properties of a convolutional code usedby the multiple chain transmitter.

An embodiment further includes constructing a plurality of Kde-interleaved sequences of confidence levels based on singular valuesper subcarrier of a plurality spatial streams of the MIMO channel,wherein the confidence levels include functions of SNRs (signal to noiseratios), wherein each of the plurality of the K de-interleaved sequencescorresponds to a one of K encoded data streams of a transmitter. Thatis, for an embodiment, the multi-chain transmitter includes N transmitchains and K encoders where source data is split into K data streams,passed through K encoders, and then “expanded” into N transmit streams.This embodiment further includes identifying a contiguous sequence ofconfidence levels in each of the plurality of de-interleaved sequences,wherein each of the confidence levels in the contiguous sequence isbelow a confidence threshold and number of confidence levels in thecontiguous sequence exceeds a run-length threshold. The reordering ofthe columns of the initial beamforming matrix of at least one of thesubcarriers reduces a number of confidence levels in contiguoussequences of the at least one of the plurality of de-interleavedsequences that are below the confidence threshold to be below therun-length threshold.

An embodiment further includes constructing a plurality of K sequencesof confidence levels based on singular values per subcarrier of aplurality spatial streams of the MIMO channel, wherein the confidencelevels include functions of SNRs (signal to noise ratios), wherein eachof the plurality of the K sequences corresponds to a one of K encodeddata streams of a transmitter. This embodiment further includescomputing an average confidence level for each of the plurality ofsequences, identifying the lowest average confidence level, wherein thereordering of the columns of the initial beamforming matrix of at leastone of the subcarriers increases the lowest average confidence level.For this embodiment, de-interleaving is not necessary because theaverage confidence level is being computed. Reordering columns on asubset of subcarriers improves the average confidence level on the worststream (and as a byproduct reduces the average confidence level on theother streams). Generally, the idea is to equalize or balance theaverage confidence levels across the multiple encoded streams. Using thede-interleaved sequence approach with checking for contiguous sequencesagainst thresholds can be more beneficial than the average confidencelevel approach, but in some situations requires more knowledge ofencoder and the inter-leaver, and may also require more latency.

An embodiment further includes constructing a de-interleaved sequence ofeffective SNRs based on singular values per subcarrier of all spatialstreams of the MIMO channel, and identifying a contiguous sequence ofeffective SNRs in the de-interleaved sequence, wherein each of theeffective SNRs in the contiguous sequence is below an SNR threshold andnumber of effective SNRs in the contiguous sequence exceeds a run-lengththreshold. The reordering of the columns of the initial beamformingmatrix of at least one of the subcarriers reduces a number of effectiveSNRs in contiguous sequences of the de-interleaved sequence that arebelow the SNR threshold to be below the run-length threshold. For anembodiment, the run-length threshold is based on properties of aconvolutional code used by the multiple chain transmitter.

An embodiment further includes cycling through a plurality of possiblepermutations for re-ordering columns of the initial beamforming matrixacross adjacent subcarrier, and repeating the cycling to cover allsubcarriers.

An embodiment further includes identifying a number of possiblepermutations of the re-ordering of columns to be a number N, dividingthe total number of subcarriers into N sets, and re-ordering columns ofthe initial beamforming matrix according to a one of the N permutationsfor at least a subset of the N sets.

At least some embodiments further include adjusting the re-ordering ofcolumns, wherein a maximum number of subcarriers across any spatialstream with a singular value less than a singular value threshold, isminimized. Based on knowledge of the code, the number of correctableerrors by the decoder can be estimated. Additionally, based on knowledgeof the modulation scheme and constellation mapper, a singular valuethreshold (SVT) can be obtained such that any subcarrier with singularvalue below the SVT is likely to yield at least one bit withsufficiently low confidence level which will require correction by thedecoder. When the singular values of a large number of subcarriers onany spatial stream fall below the SVT, there is a high likelihood ofuncorrectable errors by the decoder. Therefore, choosing a reorderingscheme which minimizes or at least reduces the maximum number ofsubcarriers for any spatial stream with singular value below the SVThelps to improve performance of the receiver.

At least some embodiments further include selecting the re-ordering ofthe columns to reduce decoding errors at a receiver of the plurality ofmulti-carrier signals as compared to decoding errors at the receiverutilizing the initial beamforming matrix.

For least some embodiments, selecting a beamforming technique includessingular value decomposition (SVD), wherein the initial beamformingmatrix includes at least one of Ascending Value SVD (AVSVD) thatincludes diagonal singular values in an increasing order, or DescendingValue SVD (DVSVD) that includes diagonal singular values in anincreasing order.

For least some embodiments, if the initial beamforming matrix includesAVSVD, then the final beamforming matrix includes DVSVD, and if theinitial beamforming matrix includes DVSVD, then the final beamformingmatrix includes AVSVD.

For least some embodiments, final beamforming matrix is determined atthe receiver and transmitted back to the multiple antenna transmitter.For least some embodiments, final beamforming matrix is determined atthe multiple antenna transmitter.

A semiconductor intellectual property core, such as a microprocessorcore, or a portion thereof, fixed function circuitry, or configurablecircuitry embodying the disclosure can be described in data stored on amachine readable medium. Such data can be in accordance with a HardwareDescription Language (HDL), and may include Register Transfer Language(RTL) description data, for example. This descriptive data can be usedto simulate, verify, and/or produce a specific implementation of thedisclosure (e.g., an integrated circuit, or a combination of integratedcircuit(s) and discrete components).

The disclosure explained example embodiments using block diagrams that,for example, show a flow of data through different functional blocks. Toa person of ordinary skill in the relevant arts, the names given tothese functional blocks also describe example structure for implementingthose functions, without including unnecessary detail. These functionalblocks can have varied implementations, including using fixed-functioncircuitry, partially configurable circuitry, special-purpose processors,such as digital signal processors, generally programmable processorcores, and combinations thereof. For example, some implementations mayimplement some of the depicted functional blocks using softwareconfiguring a processor, while others may use fixed-function circuitry.Since different implementations may use different physical hardwareelements, the depiction of particular arrangements of functional blocksdoes not imply that implementations need to have separate structuresimplementing those functions. For example, a beam forming matrixmultiplier can be implemented as a separate multiplier from processor280, but such multiplier also could be implemented as a resource sharedwith other functional blocks, or a multiplier driven by decodedinstructions from a processor (such as, processor 280).

This disclosure explains that a processor can perform certain aspects ofmethods according to the disclosure. Such processor can be a generallyprogrammable processor, which can execute machine readable codeaccording to an instruction set architecture. Such processor also canhave more limited configurability, such as allowing configurabilityusing supplied sets of parameters that modify execution of a set ofsub-routines available from a non-volatile memory, for example. Theprocessor also can include fixed-function circuitry, which caninteroperate with programmable or configurable elements of theprocessor. When such a processor is configured to perform a function oraction described in the disclosure, the processor effectively becomescircuitry for performing that function or action, even while theprocessor also can be circuitry for performing other functions oractions. As such, the term “circuitry” does not imply a singleelectrically connected set of circuits, and circuitry may befixed-function, configurable, or programmable.

Although specific embodiments have been described and illustrated, theembodiments are not to be limited to the specific forms or arrangementsof parts so described and illustrated. The described embodiments are toonly be limited by the claims.

What is claimed:
 1. A method of beamforming, comprising: generating abeamforming matrix, comprising; obtaining a channel matrix of amultiple-input, multiple-output (MIMO) channel between a multipleantenna transmitter and a receiver; determining an initial beamformingmatrix based on a singular value decomposition of the channel matrix;and generating, by a transceiver, a final beamforming matrix comprisingre-ordering columns of the initial beamforming matrix for at least onesub-carrier of a multi-carrier signal based on a signal characteristic.2. The method of claim 1, further comprising: processing a plurality ofmulti-carrier signals using the final beamforming matrix; andtransmitting the processed plurality of multi-carrier signals through aplurality of transmit chains of the multiple antenna transmitter.
 3. Themethod of claim 1, wherein the signal characteristic includes amodulation and coding scheme.
 4. The method of claim 3, wherein once themodulation and coding scheme is identified, a column re-ordering schemeis determined by accessing a look-up-table (LUT) based on the identifiedmodulation and coding scheme.
 5. The method of claim 1, wherein thecolumns of the initial beamforming matrix are re-ordered upon changes ofthe signal characteristic.
 6. The method of claim 1, further comprising:constructing de-interleaved sequences of confidence levels for eachspatial stream of a plurality spatial streams of the MIMO channel basedon singular values per subcarrier of each spatial stream, wherein theconfidence levels comprise functions of SNRs (signal to noise ratios);constructing a de-parsed sequence of confidence levels from thede-interleaved sequences; and identifying a contiguous sequence ofconfidence levels in the de-parsed sequence, wherein each of theconfidence levels in the contiguous sequence is below a confidencethreshold and number of confidence levels in the contiguous sequenceexceeds a run-length threshold; wherein the reordering of the columns ofthe initial beamforming matrix of at least one of the subcarriersreduces a number of confidence levels in contiguous sequences of thede-parsed sequence that are below the confidence threshold to be belowthe run-length threshold.
 7. The method of claim 6, wherein therun-length threshold is based on properties of a convolutional code usedby the multiple chain transmitter.
 8. The method of claim 1, furthercomprising: constructing a plurality of K de-interleaved sequences ofconfidence levels based on singular values per subcarrier of a pluralityspatial streams of the MIMO channel, wherein the confidence levelscomprise functions of SNRs (signal to noise ratios), wherein each of theplurality of the K de-interleaved sequences corresponds to a one of Kencoded data streams of the multiple antenna transmitter; andidentifying a contiguous sequence of confidence levels in at least oneof the plurality of K de-interleaved sequences, wherein each of theconfidence levels in the contiguous sequence is below a confidencethreshold and number of confidence levels in the contiguous sequenceexceeds a run-length threshold; wherein the reordering of the columns ofthe initial beamforming matrix of at least one of the subcarriersreduces a number of confidence levels in contiguous sequences of the atleast one of the plurality of K de-interleaved sequences that are belowthe confidence threshold to be below the run-length threshold.
 9. Themethod of claim 1, further comprising: constructing a plurality of Ksequences of confidence levels based on singular values per subcarrierof a plurality spatial streams of the MIMO channel, wherein theconfidence levels comprise functions of SNRs (signal to noise ratios),wherein each of the plurality of the K sequences corresponds to a one ofK encoded data streams of the multiple antenna transmitter; computing anaverage confidence level for each of the plurality of K sequences; andidentifying a lowest average confidence level of the plurality from thecomputed average confidence levels; wherein the reordering of thecolumns of the initial beamforming matrix of at least one of thesubcarriers increases the lowest average confidence level.
 10. Themethod of claim 1, further comprising: constructing a de-interleavedsequence of effective SNRs based on singular values per subcarrier ofall spatial streams of the MIMO channel; and identifying a contiguoussequence of effective SNRs in the de-interleaved sequence, wherein eachof the effective SNRs in the contiguous sequence is below an SNRthreshold and a number of effective SNRs in the contiguous sequenceexceeds a run-length threshold; wherein the reordering of the columns ofthe initial beamforming matrix of at least one subcarrier reduces anumber of effective SNRs in contiguous sequences of the de-interleavedsequence that are below the SNR threshold to be below the run-lengththreshold.
 11. The method of claim 10, wherein the run-length thresholdis based on properties of a convolutional code used by the multiplechain transmitter.
 12. The method of claim 1, further comprising cyclingthrough a plurality of possible permutations for re-ordering columns ofthe initial beamforming matrix across adjacent subcarriers, andrepeating the cycling to cover all subcarriers.
 13. The method of claim1, further comprising: identifying a number of possible permutations ofthe re-ordering of columns to be a number N; dividing a total number ofsubcarriers of the multicarrier signal into N sets; and re-orderingcolumns of the initial beamforming matrix according to a one of the Npermutations for at least a subset of the N sets.
 14. The method ofclaim 1, further comprising adjusting the re-ordering of columns,wherein the adjusting ensures that a maximum number of subcarriersacross any spatial stream with a singular value less than a threshold isreduced.
 15. The method of claim 1, further comprising selecting there-ordering of the columns to reduce decoding errors at a receiver ofthe plurality of multi-carrier signals as compared to decoding errors atthe receiver utilizing the initial beamforming matrix.
 16. The method ofclaim 1, wherein a selected initial beamforming technique includessingular value decomposition (SVD), wherein the initial beamformingmatrix includes at least one of Ascending Value SVD (AVSVD) thatincludes diagonal singular values in an increasing order, or DescendingValue SVD (DVSVD) that includes diagonal singular values in a decreasingorder.
 17. The method of claim 16, wherein if the initial beamformingmatrix comprises AVSVD, then the final beamforming matrix comprisesDVSVD, and if the initial beamforming matrix comprises DVSVD, then thefinal beamforming matrix comprises AVSVD.
 18. The method of claim 1,wherein the final beamforming matrix is determined at the receiver andtransmitted back to the multiple antenna transmitter.
 19. The method ofclaim 1, wherein the final beamforming matrix is generated at themultiple antenna transmitter.
 20. A apparatus, comprising: a pluralityof receive chains; a processor, wherein the processor is operative to:obtain a channel matrix of a multiple-input, multiple-output (MIMO)channel between a multiple antenna transmitter and the plurality ofreceive chains; determine an initial beamforming matrix based on asingular value decomposition of the channel matrix; and generate a finalbeamforming matrix comprising re-ordering columns of the initialbeamforming matrix for a selected beamforming technique for at least onesub-carrier of a multi-carrier signal based on a signal characteristic.21. The apparatus of claim 20, wherein the processor is operative to:facilitate processing a plurality of multi-carrier signals using thefinal beamforming matrix; and wherein the apparatus is operative totransmit the processed plurality of multi-carrier signals through aplurality of antennas of the multiple antenna transmitter.
 22. Theapparatus of claim 20, wherein the apparatus is operative to provide thefinal beamforming matrix to a second transceiver that includes theplurality of antennas of the multiple antenna transmitter.
 23. Theapparatus of claim 20, wherein the processor further is operative to:construct de-interleaved sequences of confidence levels for each spatialstream of a plurality spatial streams of the MIMO channel based onsingular values per subcarrier of each spatial stream, wherein theconfidence levels comprise functions of SNRs (signal to noise ratios);construct a de-parsed sequence of confidence levels from thede-interleaved sequences; and identify a contiguous sequence ofconfidence levels in the de-parsed sequence, wherein each of theconfidence levels in the contiguous sequence is below a confidencethreshold and number of confidence levels in the contiguous sequenceexceeds a run-length threshold; wherein the reordering of the columns ofthe initial beamforming matrix of at least one of the subcarriersreduces a number of confidence levels in contiguous sequences of thede-parsed sequence that are below the confidence threshold to be belowthe run-length threshold.
 24. The apparatus of claim 20, wherein therun-length threshold is based on properties of a convolutional code usedby the multiple chain transmitter.
 25. The apparatus of claim 20,wherein the processor further is operative to: construct a plurality ofK de-interleaved sequences of confidence levels based on singular valuesper subcarrier of a plurality spatial streams of the MIMO channel,wherein the confidence levels comprise functions of SNRs (signal tonoise ratios), wherein each of the plurality of the K de-interleavedsequences corresponds to a one of K encoded data streams of the multipleantenna transmitter; and identify a contiguous sequence of confidencelevels in at least one of the plurality of K de-interleaved sequences,wherein each of the confidence levels in the contiguous sequence isbelow a confidence threshold and number of confidence levels in thecontiguous sequence exceeds a run-length threshold; wherein thereordering of the columns of the initial beamforming matrix of at leastone of the subcarriers reduces a number of confidence levels incontiguous sequences of the at least one of the plurality of Kde-interleaved sequences that are below the confidence threshold to bebelow the run-length threshold.
 26. The apparatus of claim 20, whereinthe processor further is operative to: construct a plurality of Ksequences of confidence levels based on singular values per subcarrierof a plurality spatial streams of the MIMO channel, wherein theconfidence levels comprise functions of SNRs (signal to noise ratios),wherein each of the plurality of the K sequences corresponds to a one ofK encoded data streams of the multiple antenna transmitter; compute anaverage confidence level for each of the plurality of K sequences; andidentify a lowest average confidence level of the plurality from thecomputed average confidence levels; wherein the reordering of thecolumns of the initial beamforming matrix of at least one of thesubcarriers increases the lowest average confidence level.
 27. Theapparatus of claim 20, wherein the processor further is operative to:construct a de-interleaved sequence of effective SNRs based on singularvalues per subcarrier of all spatial streams of the MIMO channel; andidentify a contiguous sequence of effective SNRs in the de-interleavedsequence, wherein each of the effective SNRs in the contiguous sequenceis below an SNR threshold and a number of effective SNRs in thecontiguous sequence exceeds a run-length threshold; wherein thereordering of the columns of the initial beamforming matrix of at leastone subcarrier reduces a number of effective SNRs in contiguoussequences of the de-interleaved sequence that are below the SNRthreshold to be below the run-length threshold.
 28. The apparatus ofclaim 27, wherein the run-length threshold is based on properties of aconvolutional code used by the multiple chain transmitter.
 29. Theapparatus of claim 20, wherein the processor further is operative tocycle through a plurality of possible permutations for re-orderingcolumns of the initial beamforming matrix across adjacent subcarriers,and repeating the cycling to cover all subcarriers.
 30. The apparatus ofclaim 20, wherein the processor further is operative to: identify anumber of possible permutations of the re-ordering of columns to be anumber N; divide a total number of subcarriers of the multicarriersignal into N sets; and re-order columns of the initial beamformingmatrix according to a one of the N permutations for at least a subset ofthe N sets.
 31. The apparatus of claim 20, wherein the processor furtheris operative to adjust the re-ordering of columns, wherein theadjustment ensures that a maximum number of subcarriers across anyspatial stream with a singular value less than a threshold, isminimized.
 32. The apparatus of claim 20, wherein the processor furtheris operative to select the re-ordering of the columns to reduce decodingerrors at a receiver of the plurality of multi-carrier signals ascompared to decoding errors at the receiver utilizing the initialbeamforming matrix.